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Wave parameters set the base for the design of coastal structures. For this purpose, commonly modelled wave properties are employed. This approach is usually adequate in the open ocean conditions where variations in the wave properties are normally quite limited. The situation is different in the nearshore areas of basins of complicated shape where wave properties can be highly variable. Unfortunately, in many cases, long and sufficiently detailed wave measurements for model validation are not available. The use of default settings of wave models means that possible errors remain unknown. This approach could lead to overdimensioned structures or to structural failures. We address the magnitude of possible errors in such conditions by comparing the output of simple wave models (such as a fetch-based SMB model, the SWAN model forced with one-point homogenous wind, etc.) and a sophisticated multi-nested SWAN wave model forced with ERA-5 winds with recent wave measurements in various nearshore locations in the eastern Baltic Sea. We use records of different length over more than 10 years. While in some locations simple models or models forced with homogenous wind lead to acceptable results, in most areas more sophisticated models are needed to adequately replicate wave properties. The outcome of our analysis provides several site-specific hints for practical coastal engineering.

The phenomenon of wave set-up may substantially contribute to the formation of devastating coastal flooding in certain coastal areas. We study the appearance and properties of empirical probability density distributions of the occurrence of different set-up heights on an approximately 80 km long section of coastline near Tallinn in the Gulf of Finland, eastern Baltic Sea. The study area is often attacked by high waves propagating from various directions, and the typical approach angle of high waves varies considerably along the shore. The distributions in question are approximated by an exponential distribution with a quadratic polynomial as the exponent. Even though different segments of the study area have substantially different wave regimes, the leading term of this polynomial is usually small (between −0.005 and 0.005) and varies insignificantly along the study area. Consequently, the distribution of wave set-up heights substantially deviates from a Rayleigh or Weibull distribution (that usually reflect the distribution of different wave heights). In about three-quarters of the occasions, it is fairly well approximated by a standard exponential distribution. In about 25 % of the coastal segments, it qualitatively matches a Wald (inverse Gaussian) distribution. The Kolmogorov–Smirnov test (D value) indicates that the inverse Gaussian distribution systematically better matches the empirical probability distributions of set-up heights than the Weibull, exponential, or Gaussian distributions.

Monitoring vessel traffic in coastal regions is a key element of maritime security. For this reason, additional ways of detecting moving vessels are explored by using the unique structure of their wake waves based on pressure measurements at the seabed. The experiments are performed at a distance of about 2 km from the sailing line using novel multisensor devices called “hydromasts” that track both pressure and near-bed water flow current velocities. The main tool for the analysis is a windowed Fourier transform that produces a spectrogram of the wake structure. It is shown that time series from the pressure sensors, measured at a frequency of 100 Hz, 0.2 m above the seabed are a valid source of input data for the spectrogram technique. This technique portrays the properties of both divergent and transverse waves with an accuracy and resolution that is sufficient for the evaluation of the speed and distance of the detected vessels from the measurement device. All the detected passings are matched with vessels using automatic identification system (AIS) data. The use of several time series from synchronized multisensor systems substantially suppresses noise and improves the quality of the outcome compared to one-point measurements. Additional information about variations in the water flow in wakes provides a simple and reasonably accurate tool for rapid detection of ship passages.

We analyse a two-step mechanism for the formation of extremely high water levels in a semi-enclosed sub-basin of the Baltic Sea with the pumping of large amounts of water first into this sea and then into the Gulf of Riga. The analysis is based on hourly water level recordings at two observations sites in the gulf (Parnu and Daugavgriva) and at one station (Liepaja) on the eastern shore of the Baltic Sea proper in the period 1961–2017. The empirical distributions of the probability of occurrence of different water levels have a classic quasi-Gaussian shape but are asymmetric: elevated water levels are more likely than negative surges. The highest recorded water levels in the interior of the Gulf of Riga exceed those on the open eastern coasts of the Baltic Sea proper by more than 1 m once in 5–10 years. The time scale of generation and relaxation of such elevated levels is about one day. There is no increase in the magnitude of episodes of strongly elevated water levels in the Gulf of Riga since the 1960s. The annual average number of episodes of significant differences between the water level at Liepaja and Parnu has decreased by a factor of 1.6 whereas differences between Liepaja and Daugavgriva did not change. This pattern of changes indicates an alteration of the directional structure of winds in this area.

We study the evolution of large systems of sticky patches of pollution that float on the sea surface and are moved around by realistic wind and simulated surface currents. The study area is the Gulf of Finland in the eastern Baltic Sea that hosts extremely heavy cargo and tanker traffic. It is assumed that patches merge at collision. Collisions are enhanced by wind impact that depends on the patch size. We implement a space partitioning algorithm for fast simulations of large systems of >8000 patches and perform a series of simulations with different initial size and location of the patches. The resulting empirical distribution of the number of patches of different size is governed universally by a stretched-exponential power law f(x) = A exp (−xb). This indicates that the evolution of large systems of pollution patches on the sea surface exhibits classic self-organization and scale invariance properties. This may be the key effect explaining how the patchiness of waste in marine environment is formed under the impact of different drivers.

Time series of water level at several sites of the eastern Baltic Sea contain statistically almost impossible outliers. Their presence may considerably modify the appearance of the relevant extreme value distributions. We analyse systematically the variation in the parameters of the Generalised Extreme Value (GEV), Gumbel and Weibull distributions for extreme water levels along a 600 km coastal stretch in the north-eastern Baltic Sea. The parameters of the distributions are evaluated using a) three different methods, b) the output of two different ocean models and c) two versions of block maxima (for calendar years and for stormy seasons), and compared with similar parameters retrieved for measured water level time series at five sites. The location and scale parameters of GEV and Gumbel distributions vary smoothly by about ±30% from their average values. The variation is modest along the open shores of the Baltic Sea proper. All these parameters increase almost linearly along the southern coast of the Gulf of Finland. The absolute values of the shape parameter of the GEV distribution are mostly

Wave heights in the Baltic Sea in 1992–2015 have predominantly increased in the sea's western parts. The linear trends in the winter wave heights exhibit a prominent meridional pattern. Using the technique of Empirical Orthogonal Functions (EOF) applied to the multi-mission satellite altimetry data, we link a large part of this increase in the wave heights with the climatic indices of the Scandinavian mode, North Atlantic Oscillation, and Arctic Oscillation. The winter trends show a statistically significant negative correlation (correlation coefficient –0.47±0.19) with the Scandinavian pattern and a positive correlation with the North Atlantic Oscillation (0.31±0.22) and Arctic Oscillation (0.42±0.20). The meridional pattern is associated with more predominant north-westerly and westerly winds driven by the Scandinavian and North Atlantic Oscillation, respectively. All three climatic indices show a statistically significant time-variable correlation with Baltic Sea wave climate during the winter season. When the Scandinavian pattern's influence is strong, North Atlantic and Arctic Oscillations' effect is low and vice versa. The results are backed up by simulations using synthetic data that demonstrate that the percentage of variance retrieved using EOF analysis from the satellite-derived wave measurements is directly related to the percentage of noise in the data and the retrieved spatial patterns are insensitive to the level of noise.

We explore the basic properties of the “climate” of the field of subinertial motions with periods of 2–12 days in the Baltic Sea. The calculations are performed using the output of the Rossby Center Ocean Model RCO with a spatial resolution of 2 nautical miles for 1961–2005. The field of such motions in the Baltic Sea is strongly asymmetric, with much more energy present in the eastern regions of the sea. Spatial distributions of 5-yr average amplitudes of fluctuations of the main and seasonal pycnocline, near-bottom velocity and kinetic and potential energy reflect this asymmetry and also exhibit extensive variability on scales of a few tens of kilometers. The majority of potential energy of such motions is concentrated in a narrow nearshore strip of the sea with a typical width of

This study focuses on time scales and spatial variations of interrelations between average weather conditions and sea surface temperature (SST), and long-term changes in the SST in south-eastern Baltic Sea. The analysis relies on SST samples measured in situ four times a year in up to 17 open sea monitoring stations in Lithuanian waters in 1960–2015. A joint application of non-metric multi-dimensional scaling and cluster analysis reveals four distinct SST regimes and associated sub-regions in the study area. The increase in SST has occurred during both winter and summer seasons in 1960–2015 whereas the switch from relatively warm summer to colder autumn temperatures has been shifted by 4–6 weeks over this time in all sub-regions. The annual average air temperature and SST have increased by 0.03°C yr–1 and 0.02°C yr–1, respectively, from 1960 till 2015. These data are compared with air temperatures measured in coastal meteorological stations and averaged over time intervals from 1 to 9 weeks. Statistically significant positive correlation exists between the SST and the average air temperature. This correlation is strongest for the averaging interval of 35 days.

The wind induced coastal upwelling process often contains a mid-phase that involves coherent long-living cross-shore surface jets of cooler water. These jets extend to 40–45 km from the coast and tend to start from particular coastal locations. We develop a simple method for evaluating the depth in the water column from where the upwelled water originates. We also test the hypothesis that the development of cross-shore surface jets may be triggered by some permanent characteristics such as the bathymetry or the slope of the nearshore seabed. The analysis is performed for a strong and well-documented upwelling in the Gulf of Finland, the Baltic Sea, using high resolution bathymetry data, satellite derived sea surface temperature, surface currents measured by in situ drifters, and properties of water masses in two sampling locations. The results indicate that the cross-shore jets originate exclusively from the shore sections with much steeper slopes (>0.0075) than in the rest of the study area. The cooler water most likely origins from intermediate water masses at depths between 15 and 30 m. The resulting identification of the source depth of the upwelled water and its spatial location assists in understanding the flux of nutrients during upwelling events and their link to the onset of cyanobacteria blooms.

The present study focuses on the quantification of coastal risks associated with erosion and inundation accelerated by sea level rise and extreme storms events in the specific conditions of micro-tidal semi-enclosed seas. The main objective is to develop a measure that characterises climate-related external hazards, the exposure (of people and assets at risk of being damaged) and vulnerability of human and natural systems. This is accomplished by means of adaption of the concept of nondimensional coastal risk (or resilience) index (CRI), as a function of coastal vulnerability and exposure indices, to the conditions of sedimentary shores of the eastern Baltic Sea and testing its suitability for low-lying coastal zones considering their environmental and socio-economic characteristics. The study area is an about 45 km long coastal section of Lithuania in the south-eastern Baltic Sea. We introduce a set of locally relevant coastal vulnerability and exposure variables, apply an Analytical Hierarchy Process to calculate the criteria weights and GIS multi-criteria evaluation approach to calculate the CRI values. The coastal segments with high vulnerability often have low values of the exposure index. About 11% of the study area is under very high risk. The largest CRI values occur at a certain distance from the touristic or industrial spots near Klaipėda, around the Palanga pier and to the north of Sventoji. These coastal sectors are highly populated areas that suffer from sediments deficit due to coastal engineering structures.

Giudici, A.; Kalda, J., and Soomere, T., 2018. Joint Impact of Currents and Winds on the Patch Formation Near the Coasts of the Gulf of Finland. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 1156–1160. Coconut Creek (Florida), ISSN 0749-0208. Both coastal and offshore areas worldwide are greatly affected by the impact of large patches of floating pollution. The main mechanism of clustering of floating litter into patches is the ability of water masses to dive (e.g. during a downwelling event) whereas the litter remains on the surface. This property is quantified in terms of compressibility of the surface velocity field. When this quantity increases over a certain threshold, patchiness of floating litter may increase explosively. However, for quasi-two-dimensional flows such as typical fields of currents over shallow areas, the compressibility is typ...

Delpeche-Ellmann, N. and Soomere, T., 2018. Possible Presence of Shear Instabilities at Steep Slopes during an Upwelling Event in the Gulf of Finland, Baltic Sea. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 481–485. Coconut Creek (Florida), ISSN 0749-0208.The cooler water jets that are present during wind-induced coastal upwellings are known to become unstable after some time and develop into sub-mesoscale phenomena that contribute to the overall mixing. In this study we examine the possibility of vertical shear instabilities, in particular the Kelvin–Helmholtz instability existing in an area where steep bottom slopes are present during an upwelling event in the Gulf of Finland, Baltic Sea. The study utilizes a combination of in-situ sampling stations, satellite derived sea surface temperature (SST) data and the HIROMB model for the Baltic Sea. Examination of the velocity shear and stratification shows that it is possible for the KHI instabilities to exist most popularly at the thalweg section of the study area at a depth of 10–16 m. It is also at this exact location that the cross-shore jets were found to develop into meanders and filaments and the greatest gradient in the SST were observed. Thus these observations signal the possibility of the KHI developing in the vicinity of steep slopes and contributing to the overall mixing.

Kelpsaitė-Rimkienė, L.; Soomere, T.; Bagdanaviciūtė, I.; Nesteckitė, L., and Žalys, M., 2018. Measurements of long waves in Port of Klaipėda, Lithuania. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 761–765. Coconut Creek (Florida), ISSN 0749-0208.Port of Klaipėda is in Klaipėda Strait that connects the Curonian Lagoon with the south-eastern Baltic Sea. Its quays are well sheltered from open sea waves but the port area still hosts dangerous water level oscillations that are apparently generated in the system consisting of the Curonian Lagoon and a strait that connects the lagoon with the Baltic Sea proper. The analysis of spectral composition of these oscillations is based on continuous pressure recordings with a frequency of 4 Hz in Port of Klaipėda during the stormy season December 2016–January 2017. The majority of the energy of oscillations is concentrated in three frequencies bands. Considerable water level changes occurred owing to infragravity motions with periods >30 s ( 0.5 m, were created at lower frequencies. The recording reveals the presence of harbor oscillations with periods 30–200 s (0.005–0.03 Hz) and seiches of the Curonian Lagoon with periods >1200 s (

Kudryavtseva, N.; Pindsoo, K., and Soomere, T., 2018. Application of Non-stationary Extreme Value Modeling to Account for Trends in Extreme Water Level Changes Along the Baltic Sea Coast. In: Shim, J.-S.; Chun, I., and Lim, H.S. (eds.), Proceedings from the International Coastal Symposium (ICS) 2018 (Busan, Republic of Korea). Journal of Coastal Research, Special Issue No. 85, pp. 586–590. Coconut Creek (Florida), ISSN 0749-0208. The classic approach to extreme water levels and their return periods relies on the choice of a convenient extreme value distribution and the subsequent evaluation of its parameters. However, there is increasing evidence that these parameters vary with time owing to climate change. A novel non-stationary modeling of parameters of a generalized extreme value (GEV) distribution is implemented based on the block maximum approach, looking for linear trends in the location parameter of the GEV distribution. The analysis is performed for simulated NEMO-Nordic water level data ...

Coasts worldwide are facing enormous challenges relating to extreme water levels, inundation and coastal erosion. These challenges need to be addressed with consideration given to the need for infrastructure such as for ports and other socio-economic developments, especially for coastal tourism. Choosing the optimal decision support tools (DSTs) for coastal vulnerability and resilience assessment is a major challenge for decision-makers and coastal planners. The robustness and flexibility of coastal decision-making can be improved by using effective DSTs, particularly for the management of coastal hazards. This study provides an overview of the construction and use of decision support systems (DSSs) as combinations of DSTs, such as the commonly used multi-criteria decision analysis (MCDA) methods and an artificial neural network (ANN), integrated with a geographical information system (GIS). The experience of many researchers is that the combination of MCDA techniques based on fuzzy logic, analytical hierarchy process (AHP) and weighted linear combination (WLC), with GIS, and possibly also incorporating ANN, provides decision-makers with a comprehensive tool for efficiently calculating decision support indices (DSIs). Hybrid tools are becoming more popular and relevant among experts due to their multiple functionalities that facilitate decision-making. An integration of DSTs in a DSS and further development of DSIs provides a path for the integration of quantitative and qualitative parameters into the decision-making process, and providing materials to be used in consultation processes. An integrated DSS is more likely to produce high-quality results for decision-makers, handle the uncertainty of analysis, and extend the long-term applicability of tools employed by coastal managers.

Coastal and estuarine ecosystems are heavily influenced through floating debris pollution. This often leads to low-quality coastal water and a negative impact on ecosystem health. The fate of debris, mostly originating from land is impacted by factors including river/tidal currents, winds, waves, and density gradients. The ability to predict hotspots of accumulation of debris has a strong socio-economic importance particularly in efficient debris clean-up operations. We show this can be done using Lagrangian coherent structures (LCSs), a technique highly robust to hydrodynamic model uncertainties. Here we present a comprehensive study showing the utility of this approach to predict areas of spontaneous material accumulation in Moreton Bay, a semi-enclosed subtropical embayment on the southeast Queensland of Australia. The backward finite-time Lyapunov exponent (FTLE) is used as a diagnostic for attracting LCSs, which identifies 11 debris accumulation hotspots. The material accumulation in these identified areas is asymmetric with most events occurring during the ebb tide and most pronounced in the spring tidal cycle, indicating a strong role of outflow in debris accumulation. The impact of wind enhances a high concentration of material accumulation in 8 identified areas of Moreton Bay. Importantly, the identified hotspots, mostly in the vicinity of islands and headland, match the areas in which there is a high level of historical debris collection. This approach thus provides a useful tool for effective clean-up management of vulnerable regions and marine protected areas.

Vessel detection and localization based on wake measurements have been used extensively in aerial and satellite reconnaissance. Here, a wake-based approach for vessel localization and speed estimation is developed using a grid of pressure sensors on the seabed. The sensor array consisted of 9 devices in a 3 × 3 rectangular grid with 2.5 m spacing between the instruments. The array was deployed at a depth of 3 m approximately 2.5 km from the fairway. The pressure time series from all sensors were used to estimate vessel speed and the travelling distance of the wake by interpreting the geometry of its time-frequency representation. The wake direction and an estimate of the vessel course are calculated from the delays of the incoming wake between the sensor locations, equivalently, based on cross-correlations of the signal at neighbouring sensors. Results for single events are compared with data collected from the vessels self-reporting systems (AIS). It is concluded that a grid of pressure sensors can provide a reliable estimation of the vessel location and its speed. The presented technique makes it possible to locate ships, and their speed and course, as the next step towards a vessel traffic monitoring system based on wake recordings.

We analyze the main properties of soliton solutions to the generalized KdV equation u t + [ F ( u ) ] x + u x x x = 0 , where the leading term F ( u ) ∼ q u α , α > 0 , q ∈ R . The far field of such solitons may have three options. For q > 0 and α > 1 the analysis re-confirmed that all traveling solitons have “light” exponentially decaying tails and propagate to the right. If q 0 and α 1 , the traveling solitons (compactons) have a compact support (and thus vanishing tails) and propagate to the left. For more complicated F u and α > 1 (e.g., the Gardner equation) standing algebraic solitons with “heavy” power-law tails may appear. If the leading term of F u is negative, the set of solutions may include wide or table-top solitons (similar to the solutions of the Gardner equation), including algebraic solitons and compactons with any of the three types of tails. The solutions usually have a single-hump structure but if F u represents a higher-order polynomial, the generalized KdV equation may support multi-humped pyramidal solitons.

We explore the possibility to identify areas of intense patch formation from floating items due to systematic convergence of surface velocity fields by means of a visual comparison of Lagrangian Coherent Structures (LCS) and estimates of areas prone to patch formation using the concept of Finite-Time Compressibility (FTC, a generalisation of the notion of time series of divergence). The LCSs are evaluated using the Finite Time Lyapunov Exponent (FTLE) method. The test area is the Gulf of Finland (GoF) in the Baltic Sea. A basin-wide spatial average of backward FTLE is calculated for the GoF for the first time. This measure of the mixing strength displays a clear seasonal pattern. The evaluated backward FTLE features are linked with potential patch formation regions with high FTC levels. It is shown that areas hosting frequent upwelling or downwelling have consistently stronger than average mixing intensity. The combination of both methods, FTC and LCS, has the potential of being a powerful tool to identify the formation of patches of pollution at the sea surface., 25 Pages, 5 Figure, Accepted to be published in the Journal of Marine Systems

We employ in-situ surface drifters and satellite derived sea surface temperature data to examine the impact that an upwelling event may have on mixing and Lagrangian transport of surrounding surface waters. The test area is located near the southern coast of the Gulf of Finland where easterly winds are known to trigger intense coastal upwellings. The analysis is based on the comparison of motions of three drifters that follow the currents in the uppermost layer with a thickness of 2 m with MODIS-based sea surface temperature data and high-quality open sea wind time series. The presence of an upwelling event superseded the classic Ekman-type drift of the surface layer and considerably slowed down the average speed of surface currents in the region affected by the upwelled cold water jet and its filaments. The drifters tended to stay amidst the surrounding surface waters. The properties of mixing were evaluated using the daily rate of temperature change along several transects. The upwelled cooler water largely kept its identity during almost the entire duration of the upwelling event. Intense mixing started at a later stage of the upwelling and continued after the end of the event when the winds that have driven the entire process began to subside.

Even though semi-sheltered sea areas usually have limited wave energy resources, some regions of such basins may still be suitable for wave energy production. We provide a review of the existing wave energy studies in the Baltic Sea basin and discuss specific features and limitations for wave energy production in this water body and possible types of small-scale wave energy converters. We also extend the numerical analysis of wave energy resources in the Baltic Sea to some semi-sheltered nearshore sections that may host large levels of wave energy flux because of a specific combination of the wind regime and geometry of the sea. The test areas are located in the vicinity of the Bay of Gdansk and in the eastern Gulf of Finland. The estimates of wave energy flux rely on numerically reconstructed time series of wave properties with a spatial resolution of 5.5 km along a >200 km long coastal section. The average wave energy resource in the test areas is much lower than at the open eastern Baltic Sea coast. However, several sections of the test regions have wave energy potential comparable to fully-open nearshore areas. The onshore wave energy flux reaches 1.79 kW/m at the coast of the Sambian (Samland) Peninsula and 1.61 kW/m in selected sections of the north-eastern Gulf of Finland. These levels provide reasonable options for local wave energy production.

An extensible, low-cost drifter control unit (VELELLA) design is presented, developed for use in drifters that are deployed in inland water bodies or near-coast regions. The control unit is custom built from basic components built around a small footprint microcontroller, making use of a GPS receiver for position tracking, a Global System for Mobile Communications [Groupe SpécialMobile (GSM)] radio for data transmission, and two sensor buses to handle analog and digital data generated by an arbitrary array of external sensors. A cloud-based data collection platform has been implemented to receive and store data transmitted over general packet radio service (GPRS) from the drifter. The control unit was found to perform satisfactorily in operational testing, providing data at subhertz frequency for position and temperature during extended time. However, some issues related to temporary data loss and power consumption spikes were identified, indicating that some further development of the control unit is required to achieve a production-ready platform for extensive and prolonged field operations.

The geographical and seasonal distributions of kinematic and nonlinear parameters of long internal waves are derived from the Generalized Digital Environmental Model (GDEM) climatology for the Mediterranean Sea region, including the Black Sea. The considered parameters are phase speed of long internal waves and the coefficients at the dispersion, quadratic and cubic terms of the weakly-nonlinear Korteweg–de Vries-type models (in particular, the Gardner model). These parameters govern the possible polarities and shapes of solitary internal waves, their limiting amplitudes and propagation speeds. The key outcome is an express estimate of the expected parameters of internal waves for different regions of the Mediterranean basin.

This study examines one of the longest collection of in-situ surface drifters, deployed at different seasons for the period of 2011–2018 in the Gulf of Finland, Baltic Sea. Overall 38 drifters deployed in batches of three were designed to capture the surface drift in the uppermost 2 m layer of the sea. The properties of drifter trajectories and the effects of wind and waves on the surface drift are analysed both qualitatively and quantitatively. The overall transport is asymmetric and the prevailing direction is out of the gulf against predominant winds. The most frequent drifter speed was 0.05–0.15 m/s (49% of occurrences) and wave height less than 0.5 m (46% of occurrences). Larger drifter speeds generally occurred during periods of stronger winds and higher waves. Wave heights >0.5 m and surface drift >0.15 m/s accounted for 21% of occurrences. In some occasions relatively high drifter speeds (>0.15 m/s) occurred under low wind and in almost calm sea (wave height of 2/3 of the occasions, underlying circulation may often dominate the motions in the uppermost layer in the study area.

The closure depth indicates the depth down to which storm waves maintain a universal shape of the coastal profile. It is thus a key parameter of the coastal zones for a variety of engineering and ecosystem applications. Its values are commonly estimated with respect to the long-term mean water level. The present study re-evaluates closure depths for microtidal water bodies where the wave loads are highly correlated with the course of the water level. The test area is the eastern Baltic Sea. The closure depth is calculated for the eastern Baltic Sea coast with a resolution of 5.5 km and the vicinity of Tallinn Bay with a resolution of 0.5 km. While the classic values of closure depth are extracted from statistics of the roughest seas, the present analysis is based on single values of a proxy of the instantaneous closure depth. These values are evaluated from numerically simulated time series of wave properties and water levels. The water level-adjusted closure depths are almost equal to the classic values at the coasts of Lithuania but are up to 10% smaller at the Baltic Proper coasts of Latvia and Estonia. The difference is up to 20% in bayheads of the Gulf of Finland.

We analyse the interconnections of wind forcing and trajectories of in-situ surface drifters deployed in the Gulf of Finland in different seasons of the years 2011 and 2013. The water masses of this brackish water body are usually strongly stratified, resulting in a layered system. The drifters were designed to follow the uppermost layer of the sea with a thickness of about 2 m. The drifter speed was 2.9–6.3% of the wind speed in 2011 when the drifters were more strongly impacted by the wind, and 1.9–2.9% in 2013 after the drifters had been modified to reduce the wind impact. The trajectories of drifters varied, in many instances the drift was almost aligned with the direction towards which the wind was blowing. In some cases the motion of drifters was systematically to the left of the wind vector apparently owing to boundary effects in the gulf. While on most occasions the drift was mostly along the gulf, on several occurrences rapid across-gulf transport was observed on time scales of 6–12 days. These observations suggest that the motions in the upper layer of the Gulf of Finland (and in similar environments) are intermittently driven by two drivers: the wind impact (including the accompanying Ekman drift) under moderate and strong winds and by underlying synoptic- and basin-scale circulation patterns in weak wind conditions.

We address the possibilities of a separation of the overall increasing trend in maximum water levels of semi-enclosed water bodies into associated trends in the heights of local storm surges and basin-scale components of the water level based on recorded and modelled local water level time series. The test area is the Baltic Sea. Sequences of strong storms may substantially increase its water volume and raise the average sea level by almost 1 m for a few weeks. Such events are singled out from the water level time series using a weekly-scale average. The trends in the annual maxima of the weekly average have an almost constant value along the entire eastern Baltic Sea coast for averaging intervals longer than 4 days. Their slopes are ~4 cm/decade for 8-day running average and decrease with an increase of the averaging interval. The trends for maxima of local storm surge heights represent almost the entire spatial variability in the water level maxima. Their slopes vary from almost zero for the open Baltic Proper coast up to 5–7 cm/decade in the eastern Gulf of Finland and Gulf of Riga. This pattern suggests that an increase in wind speed in strong storms is unlikely in this area but storm duration may have increased and wind direction may have rotated.

We address the propagation and transformation of long internal breather-like wave in an idealised but realistic stratification and in the conditions matching the average summer stratification in the southern part of the Baltic Sea. The focus is on changes in the properties of the breather when the water depth increases and the coefficient at the cubic nonlinear term changes its sign, equivalently, the breather cannot exist anymore. The simulations are performed in parallel in the framework of weakly nonlinear Gardner equation and using fully nonlinear Euler equations. The amplitudes of breathers in these frameworks have slightly different courses in idealised conditions (when Earth's rotation is neglected) whereas a decrease in the amplitude is faster in the fully nonlinear simulation. The impact of the background (Earth's) rotation substantially depends on the spectral width of the initial breather. The evolution of narrow-banded breathers is almost the same for rotating and non-rotating situations but amplitudes of breathers with a wide spectrum experience substantial changes in realistic situation with the background rotation. The propagation of a narrow-banded breather along a path in the Baltic Sea over a location where the cubic nonlinear term changes its sign reveals fast disintegration of the breather into a precursor soliton and a transient dispersive wave group.

High-resolution in situ water level data is one of the core sources for the identification and understanding the reaction of the sea to climate change. We analyse digitised recordings of water level measurements from all 10 currently functioning coastal tide gauges on the Latvian shores of the Baltic proper and in the Gulf of Riga for the period of 1961–2018. The frequency and temporal coverage of measurements vary greatly for these stations. The most complete hourly data are available from Liepaja on the Baltic proper coast and from Daugavgriva in the south-eastern bayhead of the Gulf of Riga. The water level regime is analysed from the viewpoint of (i) the entire range of water level variations, (ii) empirical probability distributions of different water levels, (iii) the seasonal course of water level, (iv) trends in the annual, seasonal, and monthly means and extremes of water level (in terms of the relative and uplift corrected absolute values), and (v) correlations of the main properties of water level with the North Atlantic Oscillation (NAO Gibraltar) index. The empirical probability distributions of different water levels have become narrower in 1991–2018 compared to 1961–1990 whereas very low water levels are now less frequent. The amplitude of the seasonal course has greatly decreased over these time intervals. The annual mean and maxima of water level have increased in 1961–2018. The rate of increase is smaller than the rate of increase in the sea level in the North Atlantic suggesting that changes in the local drivers of water level mitigate the sea level rise in Latvian waters. Variations in the NAO index can explain 1/3 of the annual variability of the main properties of water level and up to 2/3 of this variability in wintertime (December–March). The changes in the statistical properties of water level are consistent with alterations to the directional structure of strong winds.

Ratsep, M.; Parnell, K.E., and Soomere, T., 2020. Detecting ship wakes for the study of coastal processes. In: Malvarez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1258–1262. Coconut Creek (Florida), ISSN 0749-0208.Wakes from contemporary vessels may affect, and in some places dominate, coastal processes in the vicinity of major shipping lanes. The analysis of the properties and impact of wakes has generally been restricted to wakes that can be visually observed in raw data. In this work, spectral analysis of the time series of single-point measurements of water surface elevation from Tallinn Bay is used to highlight the structure of ship wakes using a Short Time Fourier Transform. This method makes it possible to determine the speed and distance of a vessel from the measurement site. Wakes are detected using an algorithm based on Gabor multipliers. The results are compared with vessel passages retrieved from the Automatic Identification System (AIS) data. The algorithm detects the majority of ship wakes that can be visually recognized in spectrograms and misses only those with low signal to noise ratio or those in close proximity to another vessel wake. The calculated speed and distance are consistent with the AIS data except for high-speed vessels sailing at ≥30 knots. The results indicate that by using these techniques the detection of vessel wakes from a single-point wave record is achievable under favorable weather conditions. The methods provide an option for mitigation of the impact of ship wakes in semi-enclosed water bodies.

Kudryavtseva, N.; Raamet, A., and Soomere, T., 2020. Coastal flooding: Joint probability of extreme water levels and waves along the Baltic Sea coast. In: Malvarez, G. and Navas, F. (eds.), Global Coastal Issues of 2020. Journal of Coastal Research, Special Issue No. 95, pp. 1146–1151. Coconut Creek (Florida), ISSN 0749-0208.An accurate assessment of the joint probability of water levels and waves is crucial to establish appropriate mitigation and adaptation strategies for possible flooding and coastal erosion in countries with extensive low-lying nearshore areas. The simultaneous occurrence of large waves and high still water levels can significantly increase the risk of flooding and damage of coastal constructions. In this study, the water level extremes were retrieved from simulated high-resolution 3D NEMO-Nordic water level data along the Baltic Sea coast with a spatial resolution of 2 nautical miles (∼3.7 km) and time resolution of 1 hour. The wave height data were obtained from the numerical simulations using the WAM wave model with adjusted geostrophic wind forcing with 3 nautical miles spatial resolution and the time resolution of 1 hour. Using the Archimedean copula approach, the likelihood of joint occurrence of high water levels and wave heights was evaluated along the whole Baltic Sea coast for 1979–2007. Four distinctive regions in the Baltic Sea were identified following differences in the dependence between the sea level and wave height extremes in terms of their correlation. The Arkona basin and eastern part of the Baltic proper have low dependence (correlation coefficient

Extreme water levels in the Baltic Sea have increased much faster than the global sea level rise. We employ long-term simulations with the Rossby Centre Ocean (RCO) circulation model in 1961–2005 for the quantification of (i) spatial variability of the increase rate of water level maxima in this water body and (ii) the contribution from different water level components to this increase. The increase rates of water level maxima vary from about 1.5 to 10 mm/yr. These values do not involve the vertical crust movements. The fastest increase in water level maxima occurred in the eastern Gulf of Finland (8–10 mm/yr), Gulf of Riga (6–9 mm/yr), near Klaipėda (6–8 mm/yr) and in the south-western Baltic Sea (5–7 mm/yr). Most of the increase in these locations stems from stronger local storm surges. The upsurge of the water level maxima on the shores of Sweden and in the eastern Gulf of Bothnia is typically 3–4 mm/yr and is almost fully governed by the joint impact of global sea level rise and increase in the maximum water volume of the entire sea.

Storm surges and changes in the water volume of the entire sea, with typical time scales about a day and a few weeks, respectively, are the largest contributors to the water level variations at the eastern Baltic Sea coasts. Our analysis employs time series of sea levels numerically reconstructed using the RCO (Rossby Center, Swedish Meteorological and Hydrological Institute) ocean model for 1961–2005. The distribution for the weekly-scale water level, defined as a running average over a certain time interval, has an almost Gaussian shape. For the 8-day average the distribution of the residual, interpreted as the frequency of occurrence of local storm surges of different height, almost exactly matches the exponential distribution that can be considered as reflecting the time between events of the underlying Poisson process. The distribution of the total water level contains a few outliers that often do not match the classical statistics. All extreme values (outliers) of water level are a part of the exponential distribution of storm surges for averaging intervals longer than about 3 days. Such separation of phenomena on different temporal scales is universal for the entire eastern Baltic Sea coast. The slopes of the exponential distribution for low and high water levels are different, vary markedly along the study area and provide a useful quantification of different coastal sections with respect to the probability of coastal flooding.

Long weakly nonlinear finite-amplitude internal waves in a fluid consisting of three inviscid immiscible layers of arbitrary thickness and constant densities (stable configuration, Boussinesq approximation) bounded by a horizontal rigid bottom from below and by a rigid lid at the surface are described up to the second order of perturbation theory in small parameters of nonlinearity and dispersion. First, a pair of alternatives of appropriate KdV-type equations with the coefficients depending on the parameters of the fluid (layer positions and thickness, density jumps) are derived for the displacements of both modes of internal waves and for each interface between the layers. These equations are integrable for a very limited set of coefficients and do not allow for proper description of several near-critical cases when certain coefficients vanish. A more specific equation allowing for a variety of solitonic solutions and capable of resolving most of near-critical situations is derived by means of the introduction of another small parameter that describes the properties of the medium and rescaling of the ratio of small parameters. This procedure leads to a pair of implicitly interrelated alternatives of Gardner equation (KdV-type equations with combined nonlinearity) for the two interfaces. We present a detailed analysis of the relationships for the solutions for the disturbances at both interfaces and various regimes of the appearance and propagation properties of soliton solutions to these equations depending on the combinations of the parameters of the fluid. It is shown both the quadratic and the cubic nonlinear terms vanish for several realistic configurations of such a fluid.

We demonstrate that ships of moderate size, sailing at low depth Froude numbers (0.37-0.5) in a navigation channel surrounded by shallow banks, produce depressions with depths up to 2.5 m. These depressions (Bernoulli wakes) propagate as long-living strongly nonlinear solitary Riemann waves of depression substantial distances into Venice Lagoon. They gradually become strongly asymmetric with the rear of the depression becoming extremely steep, similar to a bore. As they are dynamically similar, air pressure fluctuations moving over variable-depth coastal areas could generate meteorological tsunamis with a leading depression wave followed by a devastating bore-like feature.

The coastal zones face much higher risks disasters and vulnerability to natural and anthropogenic forcing because of their location in extremely high-energy and rapidly developing environment. We develop and implement an updated set of indicators of coastal vulnerability that characterise relatively low-lying coastal segments with negligible tidal range but affected by substantial storm surges driven by atmospheric factors. The study area is about 90 km long coast of Lithuania in the south-eastern Baltic Sea. The classical methods for building the coastal vulnerability index (CVI) are combined with the outcome analytical hierarchical process (AHP) based approach for incorporating experts' judgements to specify the weights of used criteria. The CVI relies mostly on geological parameters (shoreline change rate, beach width/height, underwater slope, sand bars, and beach sediments) and involves only significant wave height as the representative of direct physical drivers. The selected criteria were integrated into CVI calculation using two options: (I) all criteria contribute equally, (II) each criteria may have a different contribution. Based on the weights and scores derived using AHP vulnerability maps are prepared to highlight areas with very low, low, medium, high and very high vulnerability. CVIw calculation based on option II highlighted 32% of the coast being of very high to high vulnerability, 22% of moderate vulnerability and 41% of low to very low vulnerability. Although these numbers vary to some extent depending on the viewpoint, in general about 10% of the coast in the study area is under very high risk, which calls for urgent planning and protective measures.

The wake of a ship that sails at relatively large Froude numbers usually contains a number of components of different nature and with different heights, lengths, timings and propagation directions. We explore the possibilities of the spectrogram representation of one-point measurements of the ship wake to identify these components and to quantify their main properties. This representation, based on the short-time Fourier transform, facilitates a reliable decomposition of the wake into constituent components and makes it possible to quantify their variations in the time–space domain and the energy content of each component, from very low-frequency precursor waves up to high-frequency signals within the frequency range of typical wind-generated waves. A method for estimation of the ship speed and the distance of its sailing line from the measurement site is proposed, which only uses information available within the record of the ship wake surface elevation, but where it is assumed that the wake pattern does not deviate significantly from the classical Kelvin wake structure. The wake decomposition using the spectrogram method allows investigation of the energy content that can be attributed to each individual component of the wake. We demonstrate that the majority (60–80 %) of wake energy from strongly powered large ferries that sail at depth Froude numbers${\sim}0.7$is concentrated in components that are located near the edge of the wake wedge. Finally, we demonstrate that the spectrogram representation offers a convenient way to identify a specific signature of single types of ships.

We explore the possibilities for spontaneous formation of surface patches with high concentrations of contaminants through time correlations of the convergence field and the Lagrangian transport. The test area is the Gulf of Finland, the Baltic Sea, where surface velocity fields show extensive convergence. The flow properties are extracted from 3D velocity fields simulated for 1987–1991 using the OAAS model with a resolution of 1 mile. The focus is on the spatial distribution of the areas in which the values of finite-time flow compressibility of surface velocity fields exceed the threshold for clustering of floats. The distribution of such areas is asymmetric, with likely areas of patch formation located predominantly in the southern and eastern regions of the gulf. Out of nine areas of likely patch formation, six are located along the coast in regions of frequent downwelling, while three are identified in the central region of the gulf.

The contribution of various drivers to the water level in the eastern Baltic Sea and the presence of outliers in the time series of observed and hindcast water level lead to large spreading of projections of future extreme water levels. We explore the options for using an ensemble of projections to more reliably evaluate return periods of extreme water levels. An example of such an ensemble is constructed by means of fitting several sets of block maxima (annual maxima and stormy season maxima) with a Generalised Extreme Value, Gumbel and Weibull distribution. The ensemble involves projections based on two data sets (resolution of 6 h and 1 h) hindcast by the Rossby Centre Ocean model (RCO; Swedish Meteorological and Hydrological Institute) and observed data from four representative sites along the Estonian coast. The observed data are transferred into the grid cells of the RCO model using the HIROMB model and a linear regression. For coastal segments where the observations represent the offshore water level well, the overall appearance of the ensembles signals that the errors of single projections are randomly distributed and that the median of the ensemble provides a sensible projection. For locations where the observed water level involves local effects (e.g. wave set-up) the block maxima are split into clearly separated populations. The resulting ensemble consists of two distinct clusters, the difference between which can be interpreted as a measure of the impact of local features on the water level observations.

We analyse the wave energy resource theoretically and practically available in a semi-sheltered shelf sea of moderate depth and with relatively severe but highly intermittent wave climate on the example of the Baltic Sea. The wave properties along the entire eastern Baltic Sea coast, from the Sambian (Samland) Peninsula to the eastern Gulf of Finland, are reconstructed numerically for 1970–2007 with a spatial resolution of 3 nautical miles (5.5 km) and temporal resolution of 1 h using the third generation wave model WAM. Owing to the shallowness of the sea (54 m on average) the finite-depth dispersion relation is used in the estimates of the wave energy resources in the nearshore, at depths of 7–48 m where the WAM model provides adequate results. The average wave energy flux (wave power) over the 38 years in question is about 1.5 kW/m (at selected locations up to 2.55 kW/m) in the nearshore regions of the eastern Baltic Proper but much smaller, about 0.7 kW/m, in the interior of the Gulf of Finland and the Gulf of Riga. The total theoretical wave energy resource in the entire study area is about 1.5 GW. The existing and proposed marine protected areas limit the available wave energy resource down to ∼840 MW. The production of grid energy is complicated because of extremely high intermittency and strong seasonal variation of the wave properties and frequent presence of sea ice. Although the wave energy resources are of obvious interest at some locations, their use for supplying power into the grid is questionable and probably not feasible in the conceivable future.